Is /ɑi>ɑ/ or /ɑi>i/ plausible? If so, how, including intermediate steps? Same for /ɑʉ>ɑ/, /ⱺi>i/, and /ⱺi>ⱺ/?

/ɑi/ > /ɑ/ is certainly possibly. In the East Riding of Yorkshire in the UK, standard /aɪ/ is pronounced [aː], and in South Yorkshire /aʊ/ appears as [aː]. Switch the /a/ out for /ɑ/ in those and drop the length and you're sorted.

/o̞i/ to /i/, I think, happened in the history of Greek ("iotacism", maybe?).

/o̞i/ to /o̞/ could probably happen to, in a similar manner to /ɑi/ > /ɑ/, becoming /o̞:/ at first before shortening.

How concievable is it that a future desiderative become a sort of "polite imperative"--that is "please X"

So basically, "you will turn to page 20 in your textbooks" eventually meaning effectively "please turn to page 20 in your textbooks". The basic idea is that the first, when spoken by an authority figure, is sort of an imperative command.

So basically, "you will turn to page 20 in your textbooks" eventually meaning effectively "please turn to page 20 in your textbooks". The basic idea is that the first, when spoken by an authority figure, is sort of an imperative command.

This sounds like you're working through stereotypical comedic despotic speech (Nazis, Communists, etc., but can extend to work superiors who you feel have a heavy-handed approach to management): "You vill dig a hole (and you vill enjoy it!).", which is certainly imperative in nature. I suppose that could drift into a polite imperative.

But I don't think you need the middle man. French veuillez (subjunctive/imperative of vouloir, "want") carries a polite imperative force. I can't think of a great example off the top of my head to illustrate my point, but Chinese 要 (want/need) can certainly be used in an affirmative sentence to indicate that you (really) want/need to do this with imperative underpinnings. (Negative 不要，like Latin noli/nolete - don't -- is far more extensive, I think). Even English "will", with its overlapping senses of volition and futurity, straddles the line quite comfortably. Conceivable? Ya betcha, sure.

So basically, "you will turn to page 20 in your textbooks" eventually meaning effectively "please turn to page 20 in your textbooks". The basic idea is that the first, when spoken by an authority figure, is sort of an imperative command.

This sounds like you're working through stereotypical comedic despotic speech (Nazis, Communists, etc., but can extend to work superiors who you feel have a heavy-handed approach to management): "You vill dig a hole (and you vill enjoy it!).", which is certainly imperative in nature. I suppose that could drift into a polite imperative.

Well, Chagen did say "future desiderative" in his question, even though his example came across much more like indicative. Future desiderative sounds much less despotic than indicative.

Is /ɑi>ɑ/ or /ɑi>i/ plausible? If so, how, including intermediate steps? Same for /ɑʉ>ɑ/, /ⱺi>i/, and /ⱺi>ⱺ/?

/ɑi/ > /ɑ/ is certainly possibly. In the East Riding of Yorkshire in the UK, standard /aɪ/ is pronounced [aː], and in South Yorkshire /aʊ/ appears as [aː]. Switch the /a/ out for /ɑ/ in those and drop the length and you're sorted.

It's also a common Anglo-Frisian sound change, resulting in the Bein [baɪ̯n]/bone [boːn] correspondance between English in German where the long /ɑ/ was later raised in English.

The Southern vowel shift also has ai > a:, while in Pittsburgh one hears au > a: this is just a very common sound change in English. I am guessing something internal motivates it.

I have hunch that it's because of the rareness of a-like sounds in English, with the old /a/ having fronted except in front of /r/ (The American father-bother merger is another sound change which solves that problem). Also, if /ai/ was on the way of becoming /eː/ or /ɛː/, that would likely cause a merger with /ei/, so it monophthongizes into something more open.

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A linguistics enthusiast who would like to make a conlang, but can't decide what to call what.

The Southern vowel shift also has ai > a:, while in Pittsburgh one hears au > a: this is just a very common sound change in English. I am guessing something internal motivates it.

I have hunch that it's because of the rareness of a-like sounds in English, with the old /a/ having fronted except in front of /r/ (The American father-bother merger is another sound change which solves that problem). Also, if /ai/ was on the way of becoming /eː/ or /ɛː/, that would likely cause a merger with /ei/, so it monophthongizes into something more open.

The Southern vowel shift also has ai > a:, while in Pittsburgh one hears au > a: this is just a very common sound change in English. I am guessing something internal motivates it.

I have hunch that it's because of the rareness of a-like sounds in English, with the old /a/ having fronted except in front of /r/ (The American father-bother merger is another sound change which solves that problem). Also, if /ai/ was on the way of becoming /eː/ or /ɛː/, that would likely cause a merger with /ei/, so it monophthongizes into something more open.

I doubt that, given how cluttered English is in that regard - with the trap, bath, father, palm, dog, cloth, caught, baulk, court, and cut vowels all squeezing into the area where most languages just have /a/ (and undergoing various mergers as a result).

I think a better explanation may be the structure of the phonology. Other than its broken high vowels, which may be due to overcluttering in the top corners, English doesn't seem to like any (falling) diphthongs.

So:
a) English has been merging or simplifying its diphthongs for the last thousand years
b) it's left with only a few diphthongs left. Many languages have almost as many diphthongs as possible pairs of vowels, but English only has a handful, despite having a huge number of monophthongs
c) all the remaining diphthongs (except maybe the high vowels?) are monophthongs in some dialect

So other examples of this include the "gate" and "goat" vowels (monophthongised in many dialects) and the "square", "cure" and "near" vowels (monophtongised in SSBE, in just the last couple of generations). Interestingly, the only diphthong that really seems robust - 'choice', has actually attracted monophthongs to merge with it in several dialects (most famously the old NY 'bird-boyd' merger).

Why is this? Well, I'd suggest:
- English has lots of monophthongs. What's a few more?
- English has few diphthongs, so they stick out
- English has a tendency to have long and short vowels diverge in quality. So if a diphthong wants to turn into a long vowel, there'll probably be a space for it in the system. So, for example, when "air" turned into a long /E/, that didn't cause any confusion, because short non-rhotic "E" had already moved out of the way to E\. Likewise, /eI/ can smoothe to /e:/ easily because there's no short counterpart
- the other side of that is that length isn't phonemic, so it only has a peripheral role in prosody. Some vowels are longer than others on average, but English doesn't respect a distinct "long syllable" category in terms of stress and timing. Diphthongs demand long syllables (even when unstressed), so they stick out prosodically as well. I think, prosodically, English wants to have all its stressed syllables more or less the same length, and likewise witth unstressed syllables: so to try to shorten the long vowels, it moves them out of the way of the short vowels, and then to shorten the diphthongs it turns them into new long vowels, and it tries to shorten all the long vowels, which aren't that long anyway. So... maybe it's all just the fault (like everything else in English) of the very strong stress-timing system?

Anyway, regarding /ai/ > /a:/ specifically, and to tie into a recent conversation: it's also a feature of the traditional Cumbrian dialect. And something different but related is happening in the South with some combination of the shire/shower, shire/shah and shower/shah mergers, in which /ai@/ and/or /au@/ monophthongise to /a:/, which may or may not be the same as /A/ depending on the speaker.

You're right - the lack of an a-like vowel can't be the reason for the monophthongization of /ai/ into /aː / in modern English - that "problem" is solved by the different mergers and splits of monophthongs (eg. the father-bother merger, the trap-bath split, loss of rhoticity). Frankly, I got that Idea when looking at the development of Old English, where the chronology of sound changes does suggest that it is the case: 1. West Germanic *ɑː fronts to *æː except when nasalized, 2. West Germanic *ai monophthongizes to *ɑː, filling the gap. Unlike Modern English, West Germanic had a rather small vowel system and no cluttering in the low back vowel space. I also got the stupid idea that languages somehow want to get a mid low /a/, and that similar vowels don't count - and English has plenty of those!

In Modern English, the situation, as you've said, is more like: 1. Middle English /a/ fronts to /æ/, 2. a bunch of back vowels lower to fill the gap, 3. mergers and splits happen, introducing more instances of /ɑː/. Monophthongization of /ai/, as you've said, is unlikely to be a part of the same process, and likely has a different cause.

To add to your explanation, I've noticed that the "choice" vowel is the only Modern English diphthong which continues a Middle English one - all the others are derived from monophthongs, and "face" and "goat" in particular seem to still pattern as monophthongs in many dialects (the same can be said about "fleece" and "goose" in those dialects where they are diphthongs). Since they continue to occupy roughly the same spot in the vowel space, it is easy for them to alternate between monophtongs and diphthongs without merging with another vowel. Could it be that "choice" is less prone to monophthongization because it never had a monophthongal counterpart to begin with (to say nothing about the crowdedness of the back vowel space)?

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A linguistics enthusiast who would like to make a conlang, but can't decide what to call what.

What are geminated nasals likely to turn into? Could they become prenasalized stops?

In Icelandic at least, Old Norse /n:/ becomes /tn̥/ in some environments, and I seem to recall other languages in which long nasals become pre-stopped nasals, or something similar. Wikipedia says that in West Samic languages, geminate nasals either become pre-stopped or pre-glottalised. They can also, of course, shorten, either merging with original short nasals, or the short nasals can becomes something else.

You can tell the same lie a thousand times,
But it never gets any more true,
So close your eyes once more and once more believe
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Just one time.

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I wonder if high vowels can be derived from non-high, hetero-organic vowel clusters like /a.e/ and /o.ø/ too.

I honestly hadn't even thought of that... I just went with a CV(C) structure, but, yeah, if you allow vowels adjacent to each other with no intervening consonant, then you could certainly have different vowels arise from that.

You can tell the same lie a thousand times,
But it never gets any more true,
So close your eyes once more and once more believe
That they all still believe in you.
Just one time.